In the figure above, line \(l\) is prarallel to line \(m\). If \(x=35\), what is the measure of \(\angle ADC \)?
Approach
We are given \( \angle BAD\). The other angle of \( \triangle ABD\) must be complementary.
$$ m\angle BDA = 90\degree-m\angle BAD $$
$$ 35\degree = 90 \degree - \angle BAD $$
$$ m\angle BAD = 55 \degree $$
A similar approach is used to find \( m\angle BDC\). Since \(l\) || \(m\), \(\overline{BD}\) is perpendicular to line \(m\) since is it perpendicular to line \(l\). Therefore \(m\angle BDC=55 \degree\) since the two angles divided by \(\overline{DC}\) must be complementary.
$$ m\angle ADC = 55\degree + 55\degree $$
$$ =\boxed{110 \degree} $$